11/10/2015 - 15:30

11/10/2015 - 16:30

Speaker:

Alexander Turbiner, Instituto de Ciencias Nucleares (UNAM)

Location:

CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336

Abstract:

We present a change of variables under which the elliptic Calogero Hamiltonian (a two-dimensional Lame operator) becomes an algebraic operator with polynomial coefficients. We show that the model is equivalent to the sl(3) Euler-Arnold quantum top in a magnetic field the strength of which is defined by the coupling constant. For discrete values of the coupling constant a finite number of polynomial eigenfunctions occur. A three parameter pair of commuting differential operators in two variables of degree 2 and 3 is constructed.